Question

What is the equation of the line that passes through the points (6,8) and (-3,2)

Answer 1

The point-slope form:

`y-y_1=m(x-x_1)\\\\m=(y_2-y_1)/(x_2-x_1)`

We have the points (6, 8) and (-3, 2). Substitute:

`m=(2-8)/(-3-6)=(-6)/(-9)=(2)/(3)\\\\y-8=(2)/(3)(x-6)\qquad|\text{use distributive property}\\\\y-8=(2)/(3)x-4\qquad|+8\\\\y=(2)/(3)x+4\qquad|-(2)/(3)x\\\\-(2)/(3)x+y=4\qquad|\cdot(-3)\\\\2x-3y=-12`

Answer:

point-slope form:
`y-8=(2)/(3)(x-6)`

slope-intercept form:
`y=(2)/(3)x+4`

standard form:
`2x-3y=-12`